Valen and Riordan went shopping with a total amount of $210. They had $168 left after shopping. Valen's remaining money was 3 times the amount he paid for. Riordan's remaining money was 5 times the amount he had spent.

1. How much did Riordan spend?
2. How much did Riordan bring along for shopping?

	Valen	Riordan	Total
Before	4 u	6 p	210
Change	- 1 u	- 1 p	- 42
After	3 u	5 p	168

(a)
Amount that Valen and Riordan spent
= 210 - 168
= $42

Amount that Valen and Riordan spent
= 1 u + 1 p

1 u + 1 p = 42
1 u = 42 - 1 p --- (1)

Amount that Valen and Riordan had left
= 3 u + 5 p 

3 u + 5 p = 168
3 u = 168 - 5 p --- (2)

Make u the same.

(1) _{x 3}
3 u = 126 - 3 p --- (3)

(3) = (2)
126 - 3 p = 168 - 5 p 
5 p - 3 p = 168 - 126

2 p = 42

1 p = 42 ÷ 2 = 21

Amount that Riordan spent = $21

(b)
Amount that Riordan brought along
= 6 p
= 6 x 21
= $126

Answer(s): (a) $21; (b) $126